Graph theory investigates mathematical structures consisting of vertices and edges in order to model relationships and connectivity 1, 2. A MetaGraph is a higher-level graph whose vertices are themselves graphs, with edges representing specified relations among those graphs. An Iterated MetaGraph extends this idea recursively: its vertices are MetaGraphs, thereby forming a hierarchy of graph-of-graphs structures across multiple levels. In this paper, we study new extensions called the Molecular MetaGraph and the Molecular Iterated MetaGraph, which generalize the notion of molecular graphs using the frameworks of MetaGraphs and Iterated MetaGraphs.
Toshio Fujita (Sun,) studied this question.